"They were playing soccer east of the town, not far from our houses," Dardouna, 42, said.
He said family members found the bodies at a hospital after the boys failed to come home.
A six-month-old baby was killed by shrapnel while in bed with his parents a day earlier.
Later on Thursday, another missile later struck a police post about 150m from the home of Ismail Haniyah, a Hamas leader, in the Shati refugee camp in Gaza City, killing one civilian, one fighter and wounding four other civilians, hospital officials said.
Haniyah, who has been hiding from the Israelis for weeks, was not believed to be in the area.
In a statement earlier on Thursday, Haniyah said Israel's ongoing attacks would "not weaken the steadfastness and the determination of the Palestinian people".
The violence raised the death toll to 15 the number of Palestinians killed in the Gaza Strip on Thursday and to 26, including eight children, over the past two days, according to Palestinian officials.
Three adult civilians and eight fighters were among those killed in Thursday's air strikes or by missiles fired from the ground.
Hamza al-Haya, the son of Khalil al-Haya, one of Hamas' senior figures in Gaza, was among those killed on Thursday.
Hamas said al-Haya had commanded a rocket-launching squad in northern Gaza.
The latest wave of violence began on Wednesday when an Israeli air assault killed five Hamas fighters travelling in a van.
Hamas retaliated by firing more than 40 rockets into Israel, one of the heaviest barrages in months. One rocket landed on an Israeli college campus in the southern town of Sderot, killing an Israeli man.
Israel carried out more than 10 air attacks in northern and central Gaza on Thursday, beginning just after midnight and stretching well into the afternoon, Palestinians said.
Sderot and Ashkelon
Despite the Israeli onslaught, Palestinians fired at least 10 homemade rockets into Israel, police said.
Two people were lightly wounded, including a bodyguard of Avi Dichter, the public security minister.
Dichter was not in Sderot at the time. But after he arrived, Dichter was forced to cut short a news conference when an air-raid siren went off and his guards rushed him into a concrete shelter.
Police said four foreign-made Katyusha rockets reached Ashkelon, a major city of 120,000 nearly 20km north of Gaza.
Journalists and policemen run for cover
during a rocket attack in Sderot [AFP]
Although there were no casualties, one rocket went through the roof of a crowded apartment building.
Israel has long feared that Ashkelon could soon face regular rocket attacks. Casualties have been kept relatively low because the rockets mostly land in sparsely populated areas next to the border.
In Tokyo, Condoleezza Rice, the US secretary of state, briefly met Ehud Olmert, the Israeli prime minister, and said the Hamas rocket attacks "need to stop".
She also expressed concern for the humanitarian situation in Gaza, which is suffering shortages of certain basic goods due to a blockade imposed by Israel, and urged calm on all sides.
Rice is expected to visit the Middle East next week to help push peace efforts forward.
Nabil Abu Rdainah, a spokesman for Mahmoud Abbas, the Palestinian president, who is negotiating with Israel, said in a statement its military actions "meant only one thing: the Israeli government ... aims to destroy the peace process".
Olmert said at the end of a four-day visit to Japan that "the continuous shooting of Qassam rockets against uninvolved, innocent civilians is a major threat to the stability" of Israel's political contacts with Abbas's Palestinian Authority.
He said, however, that he planned to hold another of his regular meetings with Abbas within the next two weeks.